Question

How much oil leaks from the tank in the first four hours?

Oil is leaking from a storage facility at the rate `L(t)=400e^(-.2t)` gallons per hour where t is the time in hours. How much oil leaks from the tank in the first four hours?

Answer 1

`1101.342` gallons

Explanation:

To find the amount of oil leaked in the first `4` hours, write a definite integral to express the amount of oil leaked in `4` hours.

`int_0^4L(t)color(white)(.)dt`

Simplify,

`int_0^4 400e^(-0.2t)color(white)(.)dt`

Move the constant out,

`400int_0^4 e^(-0.2t)color(white)(.)dt`

Integrate,

`400[-5e^(-0.2t)]_0^4`

Apply limits,

`400[(-5e^-0.8)-(-5)]`

Expand,

`2000-2000e^-0.8`

Evaluate,

`1101.342`